Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in PYTHON3):

Solution:
L = input()
L = L.split()
n = int(L[0])
h = int(L[1])
b = 1
alturas = []
ar = (b*h)/2
area = ar/n
haux = 0
baux = 0
aux = 0
for k in range (n-1):
    if k==0:
        haux = (area*2*h)**(1/2)
        alturas.append(haux)
        auxh = haux
    
    else:
        haux = ((area*2*h)+(auxh**2))**(1/2)
        auxh = haux
        
        alturas.append(haux)
c = str(alturas[0])
for k in range(1,n-1):
    c += ' ' +str(alturas[k])
print(c)